提出核心元素采样法，加速推荐系统中的矩阵分解计算。
Core-elements Subsampling for Alternating Least Squares
- 通过选取关键数据子集，用稀疏矩阵近似替代全量计算。
- 在保持相近精度下，计算时间显著减少。
- 适合大规模推荐系统场景，提升算法效率。
本文提出一种新颖的逐元素子集选择方法，用于交替最小二乘（ALS）算法，聚焦于含缺失值的低秩矩阵分解问题，常见于推荐系统中。尽管ALS广泛用于基于用户-物品交互数据的个性化推荐，但其重复回归操作带来的高计算成本，对大规模数据集构成显著挑战。为提升ALS效率，我们提出核心元素采样方法，选取代表性数据子集，并利用稀疏矩阵运算高效近似ALS估计。我们建立了该方法的逼近与收敛性理论保证，表明其在保持相近精度的同时，计算时间显著低于全数据ALS。大量仿真与真实世界应用验证了该方法在多种场景下的有效性，凸显其在大规模推荐系统中的潜力。
原文摘要 · Abstract (English)
In this paper, we propose a novel element-wise subset selection method for the alternating least squares (ALS) algorithm, focusing on low-rank matrix factorization involving matrices with missing values, as commonly encountered in recommender systems. While ALS is widely used for providing personalized recommendations based on user-item interaction data, its high computational cost, stemming from repeated regression operations, poses significant challenges for large-scale datasets. To enhance the efficiency of ALS, we propose a core-elements subsampling method that selects a representative subset of data and leverages sparse matrix operations to approximate ALS estimations efficiently. We establish theoretical guarantees for the approximation and convergence of the proposed approach, showing that it achieves similar accuracy with significantly reduced computational time compared to full-data ALS. Extensive simulations and real-world applications demonstrate the effectiveness of our method in various scenarios, emphasizing its potential in large-scale recommendation systems.
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